3p^2+14p+15=0

Solution for 3p^2+14p+15=0 equation:

Simplifying
3p2 + 14p + 15 = 0

Reorder the terms:
15 + 14p + 3p2 = 0

Solving
15 + 14p + 3p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(3 + p)(5 + 3p) = 0

Subproblem 1
Set the factor '(3 + p)' equal to zero and attempt to solve:

Simplifying
3 + p = 0

Solving
3 + p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + p = 0 + -3
p = 0 + -3

Combine like terms: 0 + -3 = -3
p = -3

Simplifying
p = -3
Subproblem 2
Set the factor '(5 + 3p)' equal to zero and attempt to solve:

Simplifying
5 + 3p = 0

Solving
5 + 3p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + 3p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3p = 0 + -5
3p = 0 + -5

Combine like terms: 0 + -5 = -5
3p = -5

Divide each side by '3'.
p = -1.666666667

Simplifying
p = -1.666666667
Solution
p = {-3, -1.666666667}